On large deviations for sums of discrete m-dependent random variables

10 Jan 2019 Čekanavičius Vydas Vellaisamy Palaniappan

The ratio \$P(S_n=x)/P(Z_n=x)\$ is investigated for three cases: (a) when \$S_n\$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and \$Z_n\$ is Poisson rv; (b) when \$S_n\$ is a statistic of 2-runs and \$Z_n\$ is negative binomial rv; and (c) when \$S_n\$ is statistic of \$N(1,1)\$-events and \$Z_n\$ is a binomial r.v. We also consider the approximation of \$P(S_n\geqslant x)\$ by Poisson distribution with parameter depending on \$x\$...

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